NEW YORK UNIVERSITY SCHOOL OF LAW COLLOQUIUM ON TAX POLICY AND PUBLIC FINANCE SPRING 2013

Transcription

1 NEW YORK UNIVERSITY SCHOOL OF LAW COLLOQUIUM ON TAX POLICY AND PUBLIC FINANCE SPRING 2013 Taxation, Risk, and Portfolio Choice: The Treatment of Returns to Risk Under a Normative Income Tax Jake Brooks Professor of Law Georgetown Law February 5, 2013 (Tuesday) NYU School of Law Vanderbilt Hall-208 Time: 4:00-5:50pm Number 3

2 SCHEDULE FOR 2013 NYU TAX POLICY COLLOQUIUM (All sessions meet on Tuesdays from 4-5:50 pm in Vanderbilt 208, NYU Law School) 1. January 22 David Kamin, NYU Law School, Are We There Yet?: On a Path to Closing America's Long-Run Deficit. 2. January 29 Edward McCaffery, USC Law School, Bifurcation Blues: The Problems of Leaving Redistribution Aside. 3. February 5 Jake Brooks, Georgetown Law, Taxation, Risk, and Portfolio Choice: The Treatment of Returns to Risk Under a Normative Income Tax. 4. February 12 Lilian Faulhaber, Boston University School of Law, Charitable Giving, Tax Expenditures, and the Fiscal Future of the European Union. 5. February 26 Peter Diamond, MIT Economics Department, The Case for a Progressive Tax: From Basic Research to Policy Recommendations. 6. March 5 Darien Shanske, University of California at Hastings College of Law, A Proposal for a New Property Tax Infrastructure. 7. March 12 Dhammika Dharmapala, U. of Illinois Law School, Competitive Neutrality among Debt-Financed Multinational Firms. 8. March 26 Sarah Lawsky, University of California at Irvine Law School, Unknown Probabilities and the Tax Law. 9. April 2 Alan Viard, American Enterprise Institute, Progressive Consumption Taxation: The Choice of Tax Design. 10. April 9 Brian Galle, Boston College Law School, A Nudge is a Price. 11. April 16 Leslie Robinson, Tuck Business School, Dartmouth College, Internal Ownership Structures of Multinational Firms. 12. April 23 Larry Bartels, Department of Political Science, Vanderbilt University, Inequality as a Political Issue in the 2012 Election. 13. April 30 Itai Grinberg, Georgetown Law School, A Governance Structure to Mediate the Battle Over Taxing Offshore Accounts. 14. May 7 Raj Chetty, Harvard Economics Department, Active vs. Passive Decisions and Crowd-Out in Retirement Savings Accounts: Evidence from Denmark.

3 Taxation, Risk, and Portfolio Choice: The Treatment of Returns to Risk Under a Normative Income Tax 66 TAX L. REV. (forthcoming 2013) John R. Brooks II Draft of January 14, 2013 Please do not quote or cite without permission Abstract Many articles in the legal and economic literature claim that a pure Haig-Simons income tax cannot effectively tax investment income. This is because an investor can use leverage to gross up her investments in risky assets such that the increased gain (or loss) exactly offsets any income tax (or deduction) on the returns to risk-taking. This article argues, however, that while it is possible for an investor to make such portfolio shifts, she almost certainly will not because of the increased risk of doing so. Central to any discussion of the effects of taxation on investment risk-taking is the meaning of risk itself. The central claim of this article is that a better conception of investment risk is the risk of loss and not merely the variance of returns. Applying this notion of risk one that is well supported in the finance literature but new to the taxation-and-risk literature to an investor s portfolio choice question shows that an investor will not increase her investment in risky assets by enough to offset the tax. As a result, there is an effective tax on investment risk-taking under a normative income tax. I. Introduction... 2 II. The Domar-Musgrave Result... 7 A. The Model...9 B. Taxpayer Perspective C. Government Perspective D. Assumptions and Conditions Proportionate Tax...15 Associate Professor of Law, Georgetown University Law Center. I am grateful to Jennifer Bird-Pollan, Stephen Cohen, Lillian Faulhaber, Mihir Desai, Michael Doran, Michael Graetz, Itai Grinberg, Daniel Halperin, Louis Kaplow, Wojciech Kopczuk, Alex Raskolnikov, David Schizer, Stephen Shay, Theodore Sims, Joshua Teitelbaum, David Walker, Alvin Warren, Ethan Yale, Kathryn Zeiler, and participants in workshops at Columbia Law School, Georgetown University Law Center, and Harvard Law School for helpful conversations, comments, and suggestions. I am also especially grateful for the valuable research assistance of Yingchen Luo and Eric Remijan.

4 2. Single Tax Rate Government Portfolio Policy...16 E. The Problem III. Investment Risk and Portfolio Theory...19 A. The Problems with Variance B. The Limits of the Mean-Variance Model C. Stochastic Dominance D. Loss Aversion and Safety First E. Value at Risk F. Summary IV. The Domar-Musgrave Result Under a Safety-First Risk Measure 33 A. An Income Tax Taxes Risky Returns Investor Perspective Government Perspective...35 B. A Tax on the Risk-Free Return Taxes Risky Returns Investor Perspective Government Perspective...37 C. What Is Being Taxed? D. The Risk-Free Rate E. Derivatives V. Implications for the Debate Between an Income Tax and a Consumption Tax...45 A. Differential Treatment of Labor and Capital B. Differential Treatment of Winners and Losers VI. Conclusion...49 I. Introduction It is commonly accepted in the tax law literature that a normatively pure income tax also referred to as a Haig-Simons income tax does not tax returns to risk (the Domar-Musgrave result ). 1 Under an income tax, it is argued, investors will build portfolios that generate the same after-tax return as if the tax fell only on the risk-free rate of return and exempted the risk 1 Domar and Musgrave being the progenitors of the taxation and risk literature. Evsey D. Domar & Richard A. Musgrave, Proportional Income Taxation and Risk-Taking, 58 Q.J. ECON. 388 (1944). 2

5 premium. 2 Indeed, it has been shown that, under certain strong assumptions, an income tax is equivalent to a tax only on wages plus the risk-free return to capital. 3 From this result, some scholars conclude that a normative income tax does not tax investment risk-taking at all, 4 and thus that attempts to tax returns from investment risk taking risky returns are misguided. 5 This paper will argue, by contrast, that even if a normative income tax and a tax on the risk-free return are equivalent, it does not follow that there is no tax 6 on risky returns. Under plausible assumptions about investor risk preferences a normative income tax will indeed tax risky returns. In the Domar-Musgrave result, in order to completely erase the tax on risky returns, investors must fully gross up that is, investors must reallocate their portfolios toward risky assets by enough for the increased expected return to pay the expected tax. However, an investor will fully gross 2 See, e.g., Alvin C. Warren Jr., Would a Consumption Tax be Fairer Than an Income Tax, 89 YALE L.J (1979) [hereinafter Warren, Consumption Tax]; Alvin C. Warren Jr., How Much Capital Income Taxed under an Income Tax Is Exempt under a Cash Flow Tax?, 52 TAX L. REV. 1 (1996) [hereinafter Warren, Capital Income]. For the components of capital income see infra note Louis Kaplow, Taxation and Risk Taking: A General Equilibrium Perspective, 47 NAT L TAX J. 789, (1994). 4 See, e.g., Joseph Bankman & Barbara H. Fried, Winners and Losers in the Shift to a Consumption Tax, 86 GEO. L.J. 539, (1998) ( [M]arginal returns to risk [are] arguably subject to a zero rate of tax [under an income tax]. ); Joseph Bankman & Thomas Griffith, Is the Debate Between and Income Tax and a Consumption Tax a Debate About Risk? Does It Matter?, 47 TAX L. REV. 377, 378 (1992) ( [U]nder certain assumptions, investors in risky assets are able to offset the effects of government taxation of the risk premium by changing their investment portfolios. ); Noël B. Cunningham, The Taxation of Capital Income and the Choice of Tax Base, 52 TAX. L. REV. 17, 21 (1996) ( [T]he income tax will not reach the premium a sophisticated investor receives for investing in risky investments. ); David Elkins & Christopher H. Hanna, Taxation of Supernormal Returns, 62 TAX LAW. 93, 93 (2008) ( As is generally accepted, under certain assumptions an accrual income tax system taxes the risk-free rate of return on capital but does not tax the risk premium. ); Adam H. Rosenzweig, Imperfect Financial Markets and the Hidden Costs of a Modern Income Tax, 62 SMU L. REV. 239, (2009) ( [U]nder certain assumptions, relatively simple changes by both taxpayers and the government can result in risky returns avoiding the impact of an income tax altogether. ); Daniel Shaviro, Replacing the Income Tax With a Progressive Consumption Tax, 2004 TAX NOTES 91, ( [D]ue to portfolio adjustments, an income tax fails to affect either ex ante risk premiums or ex post risky outcomes. ); David A. Weisbach, The (Non)Taxation of Risk, 58 TAX. L. REV. 1, 2 (2004). ( [I]ndividuals, even in a Haig-Simons system, can, and will, eliminate the tax on [the return to bearing risk]. ). 5 See, e.g., Cunningham, supra note 4, at 20; Deborah Schenk, Saving the Income Tax With a Wealth Tax, 53 TAX L. REV. 423, 435 (2000); Weisbach, supra note 4, at I use the term tax here to describe not only the nominal tax itself, but also the effects on expected returns due to portfolio shifts. See infra Part IV. To be clear, I am not referring to excess burden or deadweight loss. Although the full cost of the tax is partly because of portfolio shifts, those shifts also cause a direct one-to-one increase in government revenues. Thus one could think of the full tax as simply the government revenues from the policy. See, e.g., William M. Gentry & R. Glenn Hubbard, Implications of Introducing a Broad-Based Consumption Tax, 11 TAX POL Y & ECON. 1, 7 (1997). 3

6 up only if the tax does not change either a) the risk-aversion of the investor or b) the overall risk of her portfolio. Neither is the case. Even a tax on the riskfree return will make an investor poorer and thus likely to be more risk-averse than in the absence of the tax. 7 In addition and central to this article s argument the tax will expose the investors to greater risk of loss than they would assume in a world with no tax. As a result of the changes to risk aversion and portfolio risk, investors will not shift their portfolio investments sufficiently toward risky assets to offset the full effects of the income tax they will not fully gross up their investment in risky assets in order to achieve the same after-tax returns as if there were no tax. Thus, a taxpayer will end up paying an effective tax on risky returns, even under a pure normative income tax. The first effect mentioned above increased risk aversion due to lower expected wealth is often known as the wealth effect, and is a wellunderstood prediction of expected utility theory. 8 The wealth effect has been known to the economic literature on taxation and risk for some time, 9 though it makes only brief appearances in the legal literature. 10 Because the tax will necessarily reduce wealth as compared to the no-tax world, we would not expect an investor to try to recreate the same portfolio risk as before the tax. 7 This effect is described in the economic literature as decreasing relative risk aversion or decreasing absolute risk aversion, depending on the specific behaviors. The general idea is that a person with less wealth will also have less appetite for risk losing $100 is much worse for a person who only has $500 in wealth vs. $500,000. See, e.g., Louis Kaplow, Accuracy, Complexity, and the Income Tax, 14 J. L. ECON. & ORG. 61, 74 (1998); Theodore S. Sims, Capital Income, Risky Investments, and Income and Cash-Flow Taxation, at (2008) (unpublished manuscript, on file with author). 8 Expected utility theory is the standard economic account of decision-making under uncertainty. See, e.g., John A. List & Michael S. Haigh, A Simple Test of Expected Utility Theory Using Professional Traders, 102 PROC. NAT L ACAD. SCI. U.S. 945, 945 (2005) ( Expected utility (EU) theory remains the dominant approach for modeling risky decision-making and has been considered the major paradigm in decision making since World War II. ). Much of the economic literature approaches the taxation-and-risk question through an expected utility framework, with the key exception of Domar and Musgrave s paper. To be clear, in what follows below I use some tools of expected utility theory to examine the taxation-and-risk question, but my analysis is not limited to that theory. Indeed, I also rely on portfolio choice models that, while strongly supported, do not comply with all the assumptions of expected utility theory. See infra Part III. 9 See, e.g., ANTHONY B. ATKINSON & JOSEPH E. STIGLITZ, Taxation and Risk-Taking, in LECTURES ON PUBLIC ECONOMICS 97, (1980); AGNAR SANDMO, The Effects of Taxation on Savings and Risk Taking, in 1 HANDBOOK ON PUBLIC ECONOMICS 265, (Alan J. Auerbach & Martin Feldstein eds., 1985); Agnar Sandmo, Portfolio Theory, Asset Demand and Taxation: Comparative Statics with Many Assets, 44 REV. ECON. STUD. 369, 377 (1977). 10 See, e.g., Weisbach, supra note 4, at 18 (noting the existence of a wealth effect under both an income tax and a tax on the risk-free return); Sims, supra note 7; Ethan Yale, The Cary Brown Theorem and the Income Taxation of Risk: A Reappraisal (2005) (unpublished manuscript, on file with author); Lawrence Zelenak, The Sometimes-Taxation of the Returns to Risk-Bearing Under a Progressive Income Tax, 59 SMU L. REV. 879, 895 (2006). 4

7 However, there is still the question of portfolio risk itself. Much of the tax law literature approaches the taxation-and-risk question as essentially a portfolio choice question. In doing so, the literature implicitly claims that an investor will measure the risk of an investment portfolio only by its variance, that is, the volatility of potential returns around an expected return, or mean, 11 and will attempt to hold variance constant, or with a small adjustment for wealth effects. While variance 12 is a common measure of portfolio risk, however, it has well-known flaws and does not reflect actual investor risk preferences, 13 nor does it capture more rigorous conceptions of risk. 14 Indeed, even the most orthodox models of portfolio choice do not suggest that an investor should hold variance constant in the face of a tax that lowers expected returns. The major problem with variance is that it measures only volatility, and thus implies, inter alia, that a risk-averse investor dislikes above-normal returns just as much as below-normal returns. It also measures only dispersion around the mean, not the size of potential losses. Other risk measures, such as those focusing on risk of loss better capture these more realistic concerns of investment risk-taking. As this article will show, replacing variance with a downside risk measure in the Domar-Musgrave result leads to the conclusion that there is an effective tax on risky returns, and a larger one than predicted by considering the wealth effect alone. 15 Thus, this article uses more nuanced ideas of portfolio theory and risk management to correct the existing conclusion of most of the taxation-and-risk legal literature: A normative income tax will effectively tax returns to investment risk-taking. In the course of making this argument, this article will also provide the first extensive discussion in the legal literature of some of the competing conceptions and measures of investment risk that have been developed in the financial economics and mathematical risk literature, along with these 11 Variance is defined as the expected value of squared deviations from the expected return. Thus if p(s) is the probability of each scenario and r(s) is the actual return in each scenario, variance is: " 2 2 = $ p(s)[r(s) # E(r)] s See ZVI BODIE, ALEX KANE, AND ALAN J. MARCUS, INVESTMENTS 129 (9 th ed. 2011). 12 Or standard deviation, which is the square root of the variance. 13 See STEPHEN F. LEROY & JAN WERNER, PRINCIPLES OF FINANCIAL ECONOMICS 183 (2001) ( [V]ariance does not in general provide an accurate measure of risk. ); HARRY M. MARKOWITZ, PORTFOLIO SELECTION: EFFICIENT DIVERSIFICATION OF INVESTMENTS 194 (1970) (suggesting that analyses based on semi-variance, a measure of downside risk, tend to produce better portfolios than those based on [variance], but that [v]ariance is superior with respect to cost, convenience, and familiarity ); infra Part III.A. 14 See infra Part III. 15 See, e.g., Yale, supra note 10, at TK (deriving a relatively small effective tax rate under an expected utility approach to the Domar-Musgrave result). 5

8 measures particular strengths and weaknesses. 16 In addition to serving this article s arguments, this discussion is also relevant to scholars of investment management, trust, and fiduciary law, and to legal scholarship generally. The practice of law is, after all, largely about managing risk, and legal scholarship has not generally engaged with the implications of some of the more sophisticated ways of quantifying and measuring risk. If a normative income tax does in fact tax risky returns, what are the implications? The taxation-and-risk question is relevant to, among other things, the comparison between an income tax and a consumption tax, and in particular to the cash-flow tax version of a consumption tax. 17 Some scholars have argued that a normative income tax reaches so little capital income as to be vanishingly close to a cash-flow consumption tax. 18 Thus, David Weisbach argues, supporters of a more pure Haig-Simons income tax ought to in fact prefer a cash-flow consumption tax to our imperfect income tax system. 19 However, if an income tax does reach capital income, the theoretical relationship between an income tax and a cash-flow consumption tax changes in important ways. If an income tax taxes capital income, then it will raise more revenue than a cash-flow tax at the same rate, because the tax base is larger it includes labor and capital, not just labor. For the two tax systems to raise the same revenue, the cash-flow tax rate must be higher than the income tax rate. However, the additional tax will fall on wages, rather than capital income. 20 Thus, a cash-flow consumption tax places a higher burden on labor income while largely exempting capital income, while an income tax can place a lower burden on labor income because it also captures some tax revenue from capital income. While this result is consistent with the conventional view 16 See infra Part III. 17 A consumption tax means a tax levied on a tax base of consumption (as opposed to a tax levied on a tax base of income, estate size, wealth, or other tax base). Typical consumption taxes include retail sales taxes and value-added taxes (VATs), but can also include wage taxes and cash-flow taxes. To see that a wage tax is equivalent to a consumption tax, consider the Haig-Simons definition of income as consumption plus changes in wealth: Y = C + W. HENRY C. SIMONS, PERSONAL INCOME TAXATION: THE DEFINITION OF INCOME AS A PROBLEM OF FISCAL POLICY 50 (1938). Thus the difference between a consumption tax base and an income tax base is the inclusion of changes in wealth, or savings. But because total income is essentially a combination of labor income and capital income, the exemption of savings is also the difference between a comprehensive income tax and a wage tax. Thus the two are equivalent. See E. Cary Brown, Business-Income Taxation and Investment Incentives, in INCOME, EMPLOYMENT AND PUBLIC POLICY: ESSAYS IN HONOR OF ALVIN H. HANSEN 300 (1948); William D. Andrews, A Consumption-Type Or Cash Flow Personal Income Tax, 87 HARV. L. REV (1974) (showing that a cash-flow tax is a consumption tax); Kaplow, supra note 3, at 793 (showing equivalence of consumption and wage taxes). 18 See supra note See Weisbach, supra note 4, at See infra Part V.A 6

9 that a consumption tax is likely to be less progressive than an income tax in practice, to my knowledge it has not before been argued under the strong assumptions of the taxation-and-risk literature. In addition, if an investor only partially grosses up in the face of an income tax, the tax system will end up treating winners and losers differently ex post. One defense of an income tax over a consumption tax is that it focuses on ex post results, rather than ex ante expectations. 21 The existing taxation-and-risk literature challenges that view by arguing that an income tax will not be successful in reflecting ex post differences as a result of ex ante risky investments. But where there is a real, material tax on risky returns, as I argue here, we would see different treatment of winners and losers. This article proceeds as follows. Part II explains the Domar-Musgrave result and discusses why some descriptions of the result implicitly adopt variance as a measure of investment risk. Part III reviews different conceptions of investment risk, emphasizing that economists and mathematicians have long understood that variance is a simplified measure of investment risk not suited to all applications. It will also discuss other risk measures that focus instead on risk of loss, especially the increasingly dominant Value at Risk risk measure. Part IV will return to the numerical examples from Part II and show that the Domar-Musgrave result changes when using a downside risk measure. Part IV will also address the question of the appropriate risk-free rate of return. This article s argument depends in part on the risk-free rate being materially greater than zero, and there are good reasons to believe it is. Part V extends the result to consider the comparison between an income tax and a cash-flow consumption tax. Part VI concludes. II. The Domar-Musgrave Result The taxation-and-risk literature has taken several different approaches to showing the potential effects of taxation on investment risk-taking. 22 One 21 See infra Part V.B. 22 Investment income can be thought of as containing three elements: a risk-free return, a risky return, and an inframarginal return. See Cunningham, supra note 4, at 23; Gentry & Hubbard, supra note 6, at 2 (though Gentry & Hubbard consider the ex post return, and thus also consider the actual lucky return, not just the expected risk premium). The risk-free return is essentially a time-value-of-money return, and is equal to the return from investing in risk-free or virtually risk-free assets, such as U.S. Treasury bonds. The risky return is the potentially greater, but more variable, return from investing in a risky asset, such as stocks. However, the total return from a risky asset includes a risk-free, or time-value-of-money, return as well. Thus the expected risky return is essentially the risk premium above a risk-free return that investors demand from risky assets. The inframarginal return is an above-normal return, even above the risk premium, that is sometimes available because of limited, unique opportunities. See, e.g., Cunningham, supra note 4, at 23; Weisbach, supra note 4, at 19. However, in perfect capital markets (which is the setting for this model), we would not expect to see inframarginal returns. 7

10 strand of the literature essentially takes a portfolio choice approach, showing how to potentially build an optimal portfolio given an income tax (the portfolio approach ). This approach is typical in the legal literature 23 and was also used by Domar and Musgrave in their original work on the subject. 24 Another strand applies expected utility theory, the standard economic model that addresses choice under uncertainty (the expected utility approach ). This approach is more typical in the economics literature, 25 but has also appeared in the legal literature. 26 The idea of a wealth effect originates in the expected utility approach. Finally, a third strand shows the algebraic equivalence 27 of an income tax and a tax on the risk-free rate of return, but without reliance on assumptions about portfolio behavior or investor utility (the equivalence approach ). This approach is associated particularly with Louis Kaplow and Alvin Warren. 28 Each approach leads to slightly different expressions of the Domar- Musgrave result. The portfolio approach usually concludes that an income tax does not tax risky returns. 29 The expected utility approach reaches the same conclusion, provided that the risk-free rate is zero. When the risk-free rate is positive, the expected utility approach predicts a wealth effect and thus concludes that an income tax partially taxes risky returns, 30 with the degree of Such returns are essentially economic rents due to market power, particular skills, particular access to investment opportunities, or unique ideas. See Cunningham, supra note 4, at 23; Elkins & Hanna, supra note 4. As such, they are either returns to labor or returns to capital due to imperfect markets or information asymmetries. While the existence of inframarginal returns should play an important role in policy discussions, I do not consider them here, and instead focus only on risk-free and risky returns. Furthermore, inframarginal returns are thought to be taxed under a consumption tax, see Cunningham, supra note 4, at 24; Warren, Capital Income, supra note 2, at 4-6; Weisbach, supra note 4, at 23, and therefore need not be part of the comparison between a normative income tax and a normative consumption tax. 23 See, e.g., Cunningham, supra note 4; Schenk, supra note 5; Shaviro, supra note 4; Weisbach, supra note See Domar & Musgrave, supra note See supra note See Sims, supra note 7, Yale, supra note Kaplow has defined equivalence of two tax regimes for these purposes as follows: (1) in every state of nature, individuals have the same after-tax wealth in period 1 under both regimes; (2) in every state of nature, the government has the same revenue in period 1 under both regimes; and (3) total investment in each asset in period 0 is the same under both regimes. See Louis Kaplow, Taxation and Risk-Taking, NBER Working Paper No. 3079, at 6 (1991). By total investment Kaplow means the total market-wide investment in the asset. Id. n.7. Thus the fact that investors shift their portfolios does not upset the equivalence, because, as discussed below, the government makes offsetting shifts in its portfolio such that total investment is unchanged. 28 See Kaplow, supra note 3; Warren, Capital Income, supra note See, e.g., Weisbach, supra note 4, at See supra note 9. 8

11 taxation dependent on the investor s risk aversion. Finally, the equivalence approach concludes that an income tax is equivalent to a wage tax plus a tax on the risk-free return. 31 Not all of these conclusions can be true, of course (provided that the riskfree rate is positive). At first glance, it may seem that the first and third strands, the portfolio approach and the equivalence approach, reach the same conclusion: if an income tax is equivalent to a tax only on the risk-free return, then would it not follow that risky returns are untaxed? But in fact the two conclusions are not the same. Even if we assume that an income tax is equivalent to a wage tax plus a tax on the risk-free return, it does not follow that risky returns are untaxed, as this article will show. 32 The appeal of the portfolio approach is its explanatory power without resort to mathematical abstractions. As this Part will show, this approach typically involves an investor making shifts in her portfolio in response to the income tax. But therein is also the essential problem with the portfolio approach; by skipping critical math, it often skims over implicit assumptions that ignore the role of risk. Thus, writers rarely emphasize that they are assuming (unrealistically) constant relative risk aversion, 33 or that variance is their implied choice of risk measure. 34 For the sake of clarity, this article will also generally follow the portfolio approach, but while engaging the important question of risk. I begin with examples of the basic portfolio approach as typically presented in the literature, starting first with the taxpayer s perspective, then turning to the government s. However, when we return to these examples in Part IV, I will show how measuring risk differently changes the result. I will also show, however, that my conclusion does not upset the robust conclusion of the equivalence approach, that an income tax is equivalent to a wage tax plus a tax on the risk-free rate of return. A. The Model In order to isolate the effects of taxation on risk and risk-taking, the standard model used in the literature assumes a simplified and idealized version of an income tax. Thus, we assume the tax base to be comprehensive Haig-Simons income, 35 taxed on an accrual basis. 36 Furthermore, the tax must 31 See, e.g., Kaplow, supra note 3, at 792; Warren, Capital Income, supra note 2, at See infra Part IV.A. 33 But see Weisbach, supra note 4, at 18 (discussing the wealth effect where there is decreasing relative risk aversion). Constant relative risk aversion means that person will not change the portion of their wealth invested in risky assets as wealth changes. See supra note See infra notes 70 & Personal income may be defined as the algebraic sum of (1) the market value of rights exercised in consumption and (2) the change in value of the store of property rights between 9

12 be proportionate, that is, the tax allows full offsetting of losses (as opposed to the limitation of losses under the current income tax system 37 ); the tax has only a single rate; and the government participates in the market by actively managing a portfolio of risk-free and risky investments. 38 In addition, we assume only two assets, a risk-free and a risky asset (e.g., a Treasury bond and a stock) and no constraints on borrowing or lending. 39 In short, the only factors that will affect the tax are the tax rate, the risk-free rate, the return distribution on the risky asset, and the particular risk preferences of the investor. Later, I discuss the importance of some of these assumptions. 40 B. Taxpayer Perspective In brief, the intuition behind the Domar-Musgrave result is that the imposition of a proportionate income tax narrows the potential gains and losses from a risky investment, because the government takes a portion of the gains and covers a portion of the losses. The government becomes in effect a partner in the risky venture, taking on part of the risk. This, in turn, can allow investors to take on more of that risky investment, possibly enough so that the increased potential return offsets, at least somewhat, the imposition of the tax (and likewise, the increased potential loss is offset by the increased deduction for the loss). We start first with the case where the risk-free rate is 0% 41 : Example 1: Consider a risky asset A with a 50% chance of returning 30% and a 50% chance of losing 10%, and a risk-free asset B that returns 0%. There is no tax. Asset A therefore has an after-tax the beginning and end of the period in question. SIMONS, supra note 17, at 50. I.e., income is defined as consumption plus changes in wealth, or Y = C + W. See supra note In contrast to our actual realization-based system. See I.R.C. 1001(a) (calculating gain as amount realized over adjusted basis). 37 I.R.C. 1211(b), See Cunningham, supra note 4, at 32 n.56; Schenk, supra note 5, at 432 n.44; Kaplow, supra note 3, at See Kaplow, supra note 3, at See infra Part II.D. 41 For consistency with later examples I treat the investor as owning a risk-free asset that yields 0%. For example, the investor could simply hold cash as the risk-free asset. However, a more intuitive example might be where an investor held only risky assets, but could borrow at 0% to gross up. To an investor with a portfolio of risk-free assets (e.g., Treasury bonds) and risky assets, selling the risk-free assets is equivalent to borrowing, assuming that his borrowing rate is the same as the bond interest rate. In each case, the net cost to the investor is r(1 t). In the case of borrowing at r, the interest is deductible, which lowers the net after-tax cost of borrowing to r(1 t). In the case of selling bonds, the investor forgoes the after tax return of r(1 t) on the bond. From the government side, the government has to pay r on any outstanding bonds. Buying back bonds thus lowers its net costs by r times the value of the bonds repurchased. This is equivalent to not repurchasing the bonds and instead lending at r. 10

13 expected return of 10%. Thus if Investor has $100 in A and $100 in B, he has a 50% chance of earning $30 and a 50% chance of losing $10. Investor s expected return is thus $10, or 10%. Now the government imposes a 40% income tax with full loss offsets. With no changes in the portfolio, Investor s gains and losses have been cut by 40%. Investor now has a 50% chance of earning $18 (after tax) or of losing $6 (after deduction). Investor s expected portfolio return, after tax, is reduced to $6, or 6%. However, Investor can simply increase his investment in A by enough to offset the new tax (or gross up his investment). He can sell $66.67 worth of the risk-free asset B and buy $66.67 more of A. This returns his portfolio to having a 50% chance of earning $30 or of losing $10, and an expected return of $10. (30% return on $ is $50, or $30 after tax, etc.) Because in both situations the investor faces the same expected after-tax return and same return distribution, it is said that an income tax does not actually tax returns from investment risk-taking (when the risk-free rate is zero, or equivalently, when borrowing is costless 42 ). Additionally and importantly for the discussion that follows the investor s overall portfolio volatility has not changed. He still faces a 50% chance of earning $30 and a 50% chance of losing $10. Next, consider the case where there is a positive risk-free rate: Example 2: Now assume that the risk-free asset B returns the risk-free rate of 5% in all cases. Before imposition of the tax, Investor has $100 invested in A and $100 invested in B. Thus Investor has a 50% chance of his portfolio returning $35 ($30 from A and $5 from B), a 50% chance of losing $5 (-$10 from A and +$5 from B), and an expected return of $15. Now the government imposes a 40% proportionate income tax. As in the example above, Investor can sell $66.67 of B and buy $66.67 of A. If he did so, he would forgo the 5% risk-free return on that $66.67, lowering his pre-tax returns from B by $3.33 (the same pre-tax cost as if he had borrowed $66.67 at the risk-free rate in the market). Investor would then have $ invested in A, which means that the after-tax returns on A would be the same as $100 invested in A in the 42 Id. 11

14 no-tax world a 50% chance of earning $30 (.6 * $50) and a 50% chance of losing $10 (.6 * $16.67). However, the $33.33 remaining in B would earn only $1.67 before tax, which would be reduced to $1 by the tax. Thus, the overall portfolio would have a 50% chance of earning $31, a 50% chance of losing $9, and an expected return of $11. In this example, the investor s only cost is the $4 reduction in the return on the risk-free asset (the forgone $3.33 return, plus the $0.67 tax on the remaining return). But this is equivalent to a tax on the risk-free return on the entire $200 portfolio. The net risk-free return on a $200 portfolio is $10 and a 40% tax on that $10 is $4. Thus, the explanation goes, an income tax accomplishes the same thing as a tax on only the risk-free return either tax would have the same effect on the potential portfolio returns and would raise the same in tax revenue therefore, it is said, the two tax systems are equivalent. Note the steps in this reasoning, however. The examples follow the portfolio approach and conclude that $4 is raised from both an income tax and a tax only on the risk-free return, and thus that the two taxes are equivalent. Because that conclusion is the same as the conclusion of the equivalence approach of Kaplow, it is implicitly accepted that a rational taxpayer would make such portfolio shifts. But this conclusion does not necessarily follow; the equivalence shown by Kaplow means only that the after-tax results under one tax could be replicated under the other, whether the investor grosses up fully, partially, or not at all. Below, I question whether we should actually expect to see the full gross-up shown in Example 2, and thus whether $4 is the full cost of either tax. 43 Before doing so, however, we need to complete the introduction to the Domar- Musgrave result. C. Government Perspective The prior section discussed how an income tax could affect individual taxpayer behavior. There is another side of any taxation question, however government revenue. Kaplow s major contribution to the taxation-and-risk literature was to show that the an income tax was equivalent to a tax on the risk-free return not just in a partial equilibrium setting looking just at taxpayers but also in a general equilibrium setting where government behavior was also considered, at least under certain stringent assumptions. 44 As will be seen below, 45 the government side of the equation is important to this article s argument. Therefore, I briefly review it here. 43 See infra Parts II.E and IV. 44 Kaplow, supra note See infra Part IV. 12

15 The examples above assume that the investor is able to purchase as many risky assets as he would like. But this assumption raises questions: Where do these extra risky assets come from? Who does the extra lending to finance the purchases? Assuming that investors writ large would already hold all existing risky assets in the no-tax world, how can they increase their holdings further after the imposition of the income tax? 46 In Kaplow s model, the additional risky assets come from the government. The government sells risky assets in order to meet the increased demand either by selling short or by selling assets held in the government s portfolio. Furthermore, the government finances the purchases by buying back Treasury bonds, the risk-free asset. Government portfolio policy not only helps to meet the increased demand for risky assets under this model, but also has two other important effects for the general equilibrium result. First, it causes government revenue to remain equivalent under an income tax and under a tax only on the risk-free return. Second, it causes overall social risk to remain equivalent under either tax, despite the increased risk-taking by investors. First, consider government revenue. A major difference between an income tax and a tax on only the risk-free return is the source of direct government revenue from the tax. Under an income tax, the government collects a share of both risky and risk-free returns; under a tax only on the riskfree return, the government forgoes any share of risky returns. So how is it that government revenue remains constant? In the simple case where there is no expected return from risky returns the risky part of an investment is a fair bet with an equal chance of gains or losses then the tax on risky returns produces no expected revenue ex ante (nor does the government s portfolio policy). The same would be true ex post in the case where winners balanced out losers and there was no net return to risk in the market as a whole. In the case where there is a positive expected return, the investors gains would be offset by government losses. Recall that, under the Domar-Musgrave result, investors gross up their investments by enough to fund the tax on investment returns. But those additional gains come essentially out of the government s pocket. If the government sold the additional risky assets short in the market, for example, then its losses would exactly match the investors gains, a portion of which gains are going right back to the government in the 46 The comparison between a no-tax world and a world with an income tax is obviously somewhat stylized the world with no taxes also has no government. Readers may prefer to imagine simply increasing an already existing income tax. If portfolio holdings were in equilibrium under a tax, the Domar-Musgrave result implies that, if the tax were increased, portfolios would shift somewhat toward risky assets. Again, assuming investors already held all risky assets, it is not obvious where the additional risky assets would come from. There might be some private short-sellers in the market, but if the market generally assumed a positive expected return, as my examples do, there would not be enough private short-sellers to meet demand. 13

16 form of tax revenue. The government is made whole, and left in the same position as if there were no tax on investment returns. Example 3: As in Example 2, Investor sells $66.67 of B in order to purchase $66.67 more of risky asset A. Assume Investor purchases the additional assets from the government, which sells A short to Investor. Investor s total investment in A produces an expected pre-tax return of $16.67, and the investment in B produces an expected pre-tax return of $1.67, for a total pre-tax expected gain of 18.33, 40% of which $7.33 goes to the government as tax revenue. The government has an offsetting expected loss on the trade of $6.67 (by short-selling $66.67 worth of A, which had a positive expected return of 10%). However, it also receives $66.67 in cash at the beginning of the period for selling A, which, in this model, it uses to buy back B from Investor (thus giving Investor the cash to finance the purchase of B). 47 That lowers the government s interest payments by $3.33. Therefore the government earns $ $3.33 = $10.67, but loses $6.67. The government thus nets $4, which, as in the above section, is equivalent to simply levying a 40% tax on the 5% risk-free return on Investor s $200 portfolio. Second, consider social risk. The early literature on the Domar-Musgrave result concluded that an income tax increases overall private risk-taking, since, as shown above, investors increase their holdings of risky assets as a result of the tax. 48 However, under Kaplow s general equilibrium model, the increase in private holdings of risky assets is entirely offset by the fact that the government has divested itself of the same amount of risky assets. The overall amount of risky assets in the economy has not changed, merely the allocation of risky assets between private investors and the government. Thus the total social risk remains unchanged. 49 D. Assumptions and Conditions The purpose of this article is to show why even under the idealized taxation-and-risk model, an income tax does effectively tax returns to risk. This is not to say, however, that the idealized model realistically portrays our actual tax system. As noted in Part II.A, the Domar-Musgrave result, 47 Another way of saying this is the government is assumed to earn the risk-free rate on cash it receives, whether by buying back bonds, lending the money out, or financing productive investment. 48 See Domar & Musgrave, supra note 1, at ; Kaplow, supra note 3, at 789 (discussing this implication of the earlier taxation-and-risk literature). 49 Kaplow, supra note 3, at

17 particularly the Kaplow general equilibrium result, depends on several strong assumptions that do not hold in practice. To what degree the relaxation of these assumptions affects the analysis has been addressed elsewhere 50 and is not a subject of this article. Nonetheless, for purposes of thoroughness, it is worth underscoring some of these assumptions and the effects that they have. 1. Proportionate Tax For an investor to rationally make the sort of portfolio shifts described in Part II.B the government must participate in both the upside and downside of any risky investment the government becomes essentially a partner in the risky venture. If, on the other hand, the government takes a share of the upside, but without sharing the cost of any losses (by disallowing a deduction), the riskiness of the investment changes (even when using the flawed variance measure of risk). In that case, the investor would compute gain at an after-tax rate, but losses at a pre-tax rate, thus skewing the expected after-tax return downward. This would minimize her interest in taking on more risk. 51 Our current tax system allows only limited deductions for investment losses. First, all but $3000 of losses can be deducted only against capital gain, not ordinary income. 52 Second, even the netting of losses against gains is limited by the basketing of long- and short-term gain and loss, 53 and by other loss limitation rules. 54 As a result, an investor can only assume the deductibility of losses if she is confident of having sufficient capital gain to offset them, 55 which would likely only be the case for investors with substantial and diverse portfolios. Not surprisingly, many scholars have concluded that having limited or no loss offsets affects the Domar-Musgrave analysis. 56 In particular, investors are not likely to shift as much toward risky assets without the assurance that the government will also share their losses. Some have noted, however, that the inability to deduct all losses will affect different investors in different ways. 50 See, e.g., Cunningham, supra note 4, at 37-39; Schenk, supra note 5, at ; Zelenak, supra note See, e.g., ATKINSON & STIGLITZ, supra note 9, at ; Thomas Brennan, Certainty and Uncertainty in the Taxation of Risky Returns (2009) (unpublished manuscript, on file with author); Domar & Musgrave, supra note 1, at ; Schenk, supra note 5, at I.R.C. 1211(b), I.R.C See, e.g., I.R.C. 465 (at-risk limitations), 469 (passive loss limitations). 55 An additional effect is that it forces investors to realize gains in order to offset losses. That creates transaction costs for investors, as well as forgone gains due to wash sale rules and other rules limiting the ability of the investor to enter back into the investment after wiping out gains. See I.R.C (wash sale rules). 56 See, e.g., ATIKINSON & STIGLITZ, supra note 9, at ; Domar & Musgrave, supra note 1, at ; David A. Weisbach, Taxation and Risk-Taking with Multiple Rates, 57 NAT L TAX J. 229 (2004); Zelenak, supra note

18 Sophisticated investors with broad and diverse portfolios and with significant other capital income are more likely to be able to fully deduct any losses, leading to the conclusion that the ability to take advantage of the Domar- Musgave portfolio shifts in order to offset the nominal tax on risky returns is not equitably distributed among all taxpayers Single Tax Rate Related to the assumption of unlimited deductibility of losses is the assumption that there is only a single rate of tax. Indeed, the lack of proportionality is in some ways a special case of the more general fact that losses and gains can be subject to different tax rates. For example, long- and short-term gains are subject to different tax rates; 58 certain basketing rules and other limitations can raise the effective tax rate on certain investments; 59 some investment assets are not considered capital assets, and thus are subject to the progressive marginal tax rates for ordinary income; 60 and even certain capital assets are subject to different tax rates. 61 The denial of full loss offsets is essentially just applying a 0% rate to certain types of capital losses. All these factors can affect the degree to which investors are willing to increase their investment in risky assets. In general, if gains will be subject to a higher rate than losses, 62 then we would not expect an investor to fully gross up. 3. Government Portfolio Policy As discussed in Part II.C, it is essential to the Domar-Musgrave result that the government supply the market with the additional risky assets needed by investors to gross up. Otherwise, demand for risky assets would outstrip supply, driving up prices and driving down returns. As a result, additional risky assets would not be able to generate returns sufficient to cover the tax. In the examples above, Investor purchases an additional $66.67 of the risky asset in order to fund the tax on the returns to his original portfolio. It was assumed above that the marginal investment in the risky asset would also have an expected return of 10%. But if the expected return on the marginal investment shrank to only 5% because of rising share prices, there would be 57 See, e.g., Schenk, supra note I.R.C. 1(h), See supra note See, e.g., I.R.C (definition of capital asset), 475 (inventory and mark-to-market accounting for dealers in securities). 61 See, e.g., I.R.C. 1(h)(1)(B) (0% rate for low-income taxpayers), (h)(4) (28% rate for collectibles and section 1202 gain ), 11 (graduated rate on corporate income), 1231 (mixed ordinary/capital treatment for property used in a trade or business). 62 Most of the rules mentioned above are intended to limit the government s share of tax losses, so we would expect that the overall affect of the rules are to create a higher rate on gains than on losses. 16

19 essentially no net gain, since the foregone risk-free return (or, equivalently, the borrowing cost) would fully offset the incremental gain on the risky asset. This would leave the original pre-tax expected return of $10, a tax of $4, and thus an after-tax return of $6, rather than $8 as in the example. (Expected marginal returns between 5 and 10% would therefore generate after-tax returns between $6 and $8.) In reality, the government does not participate in the market in the way the model assumes, nor does anyone truly advocate that it should (though Kaplow suggests that a combination of other government actions could in theory approximate a government portfolio of risky assets). 63 Nonetheless, the notion is not unreasonable. Note that as a result of imposing the income tax, the government is newly exposed to volatile tax revenue from risky returns. We could imagine, therefore, that the government may wish to hedge that risk somewhat by selling risk into the market. 64 Nonetheless, because the government does not appear to manage its portfolio in this way, the equivalence between an income tax and a tax on the risk-free return cannot hold in practice. 65 This in turn means that an income tax does tax risky returns, even before taking into account the complications discussed below. This additional tax would, however, be the same under a normative cashflow consumption tax, assuming the other simplifying conditions of the model hold. The exemption of capital income under a cash-flow consumption tax requires the same grossing-up behavior as in the Domar-Musgrave analysis. 66 In that case, however, the grossing up is funded not by borrowing at the riskfree rate or selling risk-free assets, but by the tax deductions from expensing the amount invested. 67 But if the ability to gross up is similarly limited by the overall available pool of risky assets, and government portfolio policy does not alleviate the shortage, then we would see the same effect under a cash-flow consumption tax as under an income tax some additional tax on risky 63 For example, by shifting tax rates on capital and government expenditures in order to approximate short- and long-position returns depending on market states. See Kaplow, supra note 27, at See Gentry & Hubbard, supra note 6, at 8 ( Kaplow concludes that neither an income tax nor a consumption tax taxes risk because the government offsets the effects of both taxes on the uncertainly of government revenues by decreasing its position in risky assets and increasing its position in safe assets. ); Kaplow, supra note 3, at See Kaplow, supra note 3, at See, e.g., Andrews, supra note Briefly, a cash-flow consumption tax starts with a comprehensive income tax base (thus including income from labor and capital), but then provides for full expensing of capital investments. As Cary Brown and others have shown, full expensing of an amount invested is equivalent to full exemption of the income derived from that investment. See Brown, supra note 17. This is because the government provides a tax deduction for the amount invested. The reduction in tax from that deduction essentially funds an additional investment, which causes an additional deduction, and so on. The end result is a grossed-up investment, the additional returns from which pay for the nominal tax on any gain. See infra Part V. 17